lower bound: | 32 |
upper bound: | 34 |
Construction of a linear code [76,10,32] over GF(2): [1]: [79, 1, 39] Linear Code over GF(2) Construction from a stored generator matrix: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ] [2]: [78, 1, 39] Quasicyclic of degree 2 Linear Code over GF(2) QuasiCyclicCode of length 78 with generating polynomials: x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^32 + x^31 + x^30 + x^29 + x^28 + x^27 + x^26 + x^25 + x^24 + x^23 + x^22 + x^21 + x^20 + x^19 + x^18 + x^17 + x^16 + x^15 + x^14 + x^13 + x^12 + x^11 + x^10 + x^9 + x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 0 [3]: [78, 12, 32] Quasicyclic of degree 2 Linear Code over GF(2) QuasiCyclicCode of length 78 with generating polynomials: x^38 + x^37 + x^36 + x^35 + x^34 + x^33 + x^31 + x^30 + x^29 + x^28 + x^27 + x^24 + x^23 + x^21 + x^19 + x^18 + x^17 + x^15 + x^14 + x^12 + x^9 + x^7 + x^6 + x^3, x^38 + x^37 + x^35 + x^29 + x^27 + x^25 + x^21 + x^20 + x^16 + x^15 + x^14 + x^11 + x^9 + x^8 + x^7 + x^2 [4]: [78, 13, 31] Quasicyclic of degree 2 Linear Code over GF(2) The Vector space sum: [3] + [2] [5]: [79, 13, 32] Linear Code over GF(2) ExtendCode [4] by 0 [6]: [79, 14, 31] Linear Code over GF(2) The Vector space sum: [5] + [1] [7]: [80, 14, 32] Linear Code over GF(2) ExtendCode [6] by 1 [8]: [76, 10, 32] Linear Code over GF(2) Shortening of [7] at { 77 .. 80 } last modified: 2001-02-04
Lb(76,10) = 32 is found by taking a subcode of: Lb(76,12) = 32 is found by adding a parity check bit to: Lb(75,12) = 31 GG1 Ub(76,10) = 34 follows by a one-step Griesmer bound from: Ub(41,9) = 16 follows by a one-step Griesmer bound from: Ub(24,8) = 8 otherwise adding a parity check bit would contradict: Ub(25,8) = 9 YH1
YH1: Øyvind Ytrehus & Tor Helleseth, There is no binary [25,8,10] code, IEEE Trans. Inform. Theory 36 (May 1990) 695-696.
Notes
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